Question

Find the angle between the vectors u= −3,1
and v= 2,4

Answer 1

Take dot product between two vector

Answer 2

\[\alpha = \cos^{-1} \frac{ (-3 \times 2 ) + (1 \times 4 ) } { \sqrt{(-3)^2 +1^2 } \times \sqrt{2^2 +4^2} } \]

Answer 3

hm
if i get arccos 10/root(200) how do i change \[\sqrt{200}\] to something easier?

Answer 4

dot product ftw

Answer 5

You can also use a ruler to check your answer

Answer 6

a protractor ruler

Answer 7

\[\sqrt{200}=\sqrt{100*2}=10\sqrt{2}\]

Answer 8

\[\alpha=\cos^{-1}\frac{-2}{10*\sqrt{2}}=\cos^{-1}\frac{-2*\sqrt{2}}{10*\sqrt{2}*\sqrt{2}}=\cos^{-1}\frac{-2\sqrt{2}}{20}=\cos^{-1}(\frac{-\sqrt{2}}{10})\]

Answer 9

You can actually find the angle of both using trigonometry then find the difference between both angles....if you didn't know that dot product formula